Dividing Decimals Long Division Calculator

Dividing Decimals Long Division Calculator – Step-by-Step (2025)

Struggling with dividing decimals using long division? This guide walks you through the rules, placement of the decimal point, and how to recognize repeating decimals. It’s built to help you learn and check your answers in 2025.

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Why Dividing Decimals Confuses Students

With whole numbers, long division is straightforward. But with decimals, you must shift the decimal and track its position in the quotient. Missing this step is the most common cause of errors.

Takeaway: Always clear the divisor’s decimal first, then divide normally.

Step-by-Step Rules

Check the divisor. If it has a decimal, shift it right until it becomes a whole number.
Shift the dividend the same number of places to keep the problem equivalent.
Divide using long division (divide → multiply → subtract → bring down).
Place the decimal in the quotient directly above the decimal in the shifted dividend.
Extend with zeros if needed to complete the division or show repeating decimals.

Pro Tip: A divisor like 0.25 becomes 25 (two places right). Move the dividend two places too.

Worked Example #1 — 7.2 ÷ 0.4

Shift divisor: 0.4 → 4 (1 place). Shift dividend: 7.2 → 72.
Now compute 72 ÷ 4 = 18.

Answer: 7.2 ÷ 0.4 = 18

Check: Multiply back: 18 × 0.4 = 7.2 ✔

Worked Example #2 — 15 ÷ 0.25

Shift divisor: 0.25 → 25 (2 places). Shift dividend: 15.00 → 1500.
Divide 1500 ÷ 25 = 60.

Answer: 15 ÷ 0.25 = 60

Pro Tip: Dividing by a decimal smaller than 1 actually makes the quotient larger.

Worked Example #3 — 10 ÷ 3 (Repeating)

Divisor is already whole. Divide: 10 ÷ 3 = 3.333… repeating. Write as 3.(3).

Answer: 10 ÷ 3 = 3.(3)

Common Mistakes to Avoid

Forgetting to shift the dividend when clearing the divisor’s decimal.
Placing the decimal in the wrong spot in the quotient.
Stopping without showing the repeating cycle.
Mixing up multiplication checks (always verify: Divisor × Quotient ≈ Dividend).

Takeaway: Shift first, place decimal carefully, and always check with multiplication.

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FAQ: Dividing Decimals with Long Division

How do I divide a decimal by a decimal?

Shift the divisor right until it’s a whole number, then shift the dividend the same amount. Divide as normal, placing the decimal directly above in the quotient.

What if the answer is a repeating decimal?

Keep dividing until the same remainder reappears. That’s your repeating block. Write it in parentheses like 0.(142857).

Why is my answer bigger when dividing by 0.25?

Because dividing by a number less than 1 increases the result. For example, 15 ÷ 0.25 = 60.

Can I check if I got it right?

Yes—multiply your quotient by the divisor. If it matches the dividend, your work is correct.

How do I handle negative decimals?

Divide absolute values normally. Then assign a negative sign if the dividend and divisor have opposite signs.